Put mushrooms in a 4 1/2- to 6-quart cooker. Lightly sprinkle pepper over chicken. Add chicken to cooker. Top with prosciutto. Combine in a small bowl chicken broth, brandy, and thyme. Add to mixture in cooker.

Cover and cook on low-heat setting for 5 to 6 hours or on high-heat setting for 2 1/2 to 3 hours.

Remove chicken and mushrooms to a serving platter, reserving cooking liquid. Cover chicken and mushrooms with foil to keep warm.

For sauce, pour cooking liquid into a medium saucepan. Combine in small bowl the cornstarch and water. Add to liquid in saucepan. Cook and stir over medium-high heat until thickened and bubbly. Cook and stir for 2 minutes. Add cream cheese and half-and-half, whisking until smooth. Serve sauce with chicken.